1. Field of the Invention
The present invention relates to the production of pulse width modulation tonal effects in a computor organ.
2. Description of the Prior Art
The inventor's U.S. Pat. No. 3,809,786 entitled COMPUTOR ORGAN discloses an electronic musical instrument in which tones are synthesized by separately evaluating the individual Fourier components that comprise a musical waveshape. These are summed to obtain in real time the waveshape amplitudes at successive sample points. In other words, the computor organ generates tones in the frequency domain, allocating separate time slots for evaluation of the constituent frequency components of the tone.
In contrast, an analog tone generator operates basically in the time domain. For example, such an analog instrument may produce a pulse train in which the pulse repetition rate establishes the fundamental frequency f of the produced note, and wherein the pulse shape and duty cycle determine the frequency spectral content of the tone.
This is illustrated in FIG. 1 for the case of an analog tone generator which produces rectangular pulses at a repetition rate or fundamental frequency f. As is known, the spectral content of such a rectangular wave is obtained by Fourier transform, where the Fourier or harmonic coefficients are given by: ##EQU1## where .tau. is the width of each pulse, T=1/f is the pulse repetition period, A is the amplitude of the pulse and C.sub.m is the amplitude of the m.sup.th order harmonic component. The spectrum will have its zero points at harmonics: EQU m=k(T/.tau.) (Equation 2)
where k=1,2,3, . . .
A typical harmonic spectrum for the rectangular pulse train of FIG. 1 is shown in FIG. 2. In this example, the first zero f.sub.c.sbsb.1 is at m=16 for the case where the nominal pulse width .tau..sub.o =T/16. For equations 1 and 2 it is assumed that the pulse width .tau..ltoreq.(T/2).
If the pulse width .tau. is increased to a value .tau.&gt;.tau..sub.o, the frequency of the first zero decreases from f.sub.c.sbsb.1 to f.sub.c.sbsb.2, as illustrated in FIG. 3 which shows the amplitude envelope of the harmonic spectrum (FIG. 2) defined by equation 1. Conversely, if the pulse width .tau. is decreased to a value less than the nominal width .tau..sub.o, the frequency of the first zero increases from f.sub.c.sbsb.1 to f.sub.c.sbsb.3.
In a pulse type analog tone generator, modulation effects similar to vibrato may be introduced by varying the pulse width .tau. at the rate (about 5Hz to 8Hz) generally used for vibrato. An object of the present invention is to simulate pulse-type tone generation, both with and without pulse width modulation effects, in a computor organ. Another object of the present invention is to implement modulation of the set of harmonic coefficients used to establish the Fourier component relative amplitudes in a computor organ.